Details
| Original language | English |
|---|---|
| Pages (from-to) | 143-162 |
| Number of pages | 20 |
| Journal | Journal of Multivariate Analysis |
| Volume | 75 |
| Issue number | 1 |
| Publication status | Published - Oct 2000 |
Abstract
For a distribution μ on the unit interval we define the associated perpetuity Ψ(μ) as the distribution of 1+X1+X1X2+X1X2X 3+..., where (Xn)n∈N is a sequence of independent random variables with distribution μ. Such quantities arise in insurance mathematics and in many other areas. We prove the differentiability of the perpetuity functionalψ with respect to integral and supremum norms. These results are then used to investigate the statistical properties of empirical perpetuities, including the behaviour of bootstrap confidence regions.
Keywords
- Asymptotic normality, Bootstrap, Empirical perpetuities, Perpetual annuity
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Mathematics(all)
- Numerical Analysis
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Journal of Multivariate Analysis, Vol. 75, No. 1, 10.2000, p. 143-162.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Statistical Aspects of Perpetuities
AU - Grübel, Rudolf
AU - Pitts, Susan M.
PY - 2000/10
Y1 - 2000/10
N2 - For a distribution μ on the unit interval we define the associated perpetuity Ψ(μ) as the distribution of 1+X1+X1X2+X1X2X 3+..., where (Xn)n∈N is a sequence of independent random variables with distribution μ. Such quantities arise in insurance mathematics and in many other areas. We prove the differentiability of the perpetuity functionalψ with respect to integral and supremum norms. These results are then used to investigate the statistical properties of empirical perpetuities, including the behaviour of bootstrap confidence regions.
AB - For a distribution μ on the unit interval we define the associated perpetuity Ψ(μ) as the distribution of 1+X1+X1X2+X1X2X 3+..., where (Xn)n∈N is a sequence of independent random variables with distribution μ. Such quantities arise in insurance mathematics and in many other areas. We prove the differentiability of the perpetuity functionalψ with respect to integral and supremum norms. These results are then used to investigate the statistical properties of empirical perpetuities, including the behaviour of bootstrap confidence regions.
KW - Asymptotic normality
KW - Bootstrap
KW - Empirical perpetuities
KW - Perpetual annuity
UR - http://www.scopus.com/inward/record.url?scp=0042494540&partnerID=8YFLogxK
U2 - 10.1006/jmva.1999.1890
DO - 10.1006/jmva.1999.1890
M3 - Article
AN - SCOPUS:0042494540
VL - 75
SP - 143
EP - 162
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
SN - 0047-259X
IS - 1
ER -